[iasmath-seminars] Updates to this week's Mathematics Seminar schedule

Mon Mar 18 15:11:02 EDT 2019

INSTITUTE FOR ADVANCED STUDY

School of Mathematics

Princeton, NJ 08540

Mathematics Seminars

Week of March 18, 2019

--------------

Please note:

.         Talk information added to the 3/19 Symplectic Dynamics Working
Group.

.         There will be an additional Symplectic Dynamics/Geometry Seminar
on Wednesday, 3/20. 

The following seminars have been cancelled:

.         Working Group on Geometric Applications of the Langlands
Correspondence

.         Joint IAS/Princeton University Number Theory Seminar

--------------

Monday, March 18

Symplectic Dynamics/Geometry Seminar

Topic:                    Minimal Sets and Properties of Feral
Pseudoholomorphic Curves

Speaker:              Joel Fish, University of Massachusetts Boston

Time/Room:       3:30pm - 5:00pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=137961>
http://www.math.ias.edu/seminars/abstract?event=137961

Joint IAS/Princeton University Algebraic Geometry Seminar

Speaker:              no seminar

Time/Room:       5:00pm - 6:00pm/no seminar

Tuesday, March 19

Computer Science/Discrete Mathematics Seminar II

Topic:                    A Brief Tour of Proof Complexity: Lower Bounds and
Open Problems

Speaker:              Toniann Pitassi, University of Toronto; Visiting
Professor, School of Mathematics

Time/Room:       10:30am - 12:30pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=129148>
http://www.math.ias.edu/seminars/abstract?event=129148

Variational Methods in Geometry Seminar

Topic:                    Gap and index estimates for Yang-Mills connections
in 4-d

Speaker:              Matthew Gursky, University of Notre Dame

Time/Room:       1:00pm - 3:00pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=141224>
http://www.math.ias.edu/seminars/abstract?event=141224

Symplectic Dynamics Working Group

Topic:                    Properties of Feral Pseudoholomorphic Curves

Speaker:              Joel Fish, University of Massachusetts Boston

Time/Room:       1:30pm - 3:00pm/Simonyi Hall Classroom 114

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=143024>
http://www.math.ias.edu/seminars/abstract?event=143024

Variational Methods in Geometry Seminar

Topic:                    Multiplicity One Conjecture in Min-max theory

Speaker:              Xin Zhou, University of California, Santa Barbara;
Member, School of Mathematics

Time/Room:       3:30pm - 5:30pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=141227>
http://www.math.ias.edu/seminars/abstract?event=141227

Wednesday, March 20

BYOP at Lunch Working Group

Time/Room:       12:30pm - 1:30pm/Dilworth Room

Symplectic Dynamics/Geometry Seminar

Topic:                    Equivariant and nonequivariant contact homology

Speaker:              Jo Nelson, Rice University

Time/Room:       2:00pm - 3:00pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=143827>
http://www.math.ias.edu/seminars/abstract?event=143827

Working Group on Geometric Applications of the Langlands Correspondence

Time/Room:       3:30pm - 5:30pm/Simonyi Hall 101

Mathematical Conversations

Topic:                    from dynamics to contact topology and back

Speaker:              Jo Nelson

Time/Room:       6:00pm - 7:30pm/White Levy Room

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=141584>
http://www.math.ias.edu/seminars/abstract?event=141584

Thursday, March 21

Venkatesh Working Group

Time/Room:       10:00am - 12:00pm/Simonyi Hall 101

Analysis Seminar

Topic:                    Front propagation in a nonlocal reaction-diffusion
equation

Speaker:              Olga Turanova, University of California, Los Angeles;
Visitor, School of Mathematics

Time/Room:       1:00pm - 2:00pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=142513>
http://www.math.ias.edu/seminars/abstract?event=142513

Working Seminar in Algebraic Number Theory

Speaker:              No Seminar

Time/Room:       2:15pm - 4:15pm/No Seminar

Joint IAS/Princeton University Number Theory Seminar

Speaker:              TBD

Time/Room:       4:30pm - 5:30pm/TBD

1 An Application of the Universality Theorem for Tverberg Partitions 
   Imre Barany 

We show that, as a consequence of a remarkable new result of Attila P\'or on
universal Tverberg partitions, any large-enough set $P$ of points in $\Re^d$
has a $(d+2)$-sized subset whose Radon point has half-space depth at least
$c_d \cdot |P|$, where $c_d \in (0, 1)$ depends only on $d$. We then give an
application of this result to computing weak $\eps$-nets by random sampling.
Joint work with Nabil Mustafa.

http://www.math.ias.edu/seminars/abstract?event=128912

2 Tracking trajectories in Hamiltonian systems using holomorphic curve
tools. 
   Barney Bramham 

The goal is to describe how techniques from symplectic dynamics can be used
to study orbit travel in three dimensions, for systems like the restricted
3-body problem from celestial mechanics. The pseudo-holomorphic curve theory
initiated by Hofer, Wysocki and Zehnder gives a decomposition of the space
into regions whose boundaries are surfaces transverse to the flow.
(Pseudo-holomorphic curves are special minimal surfaces). One can label the
regions A, B, C etc and form a directed graph. This gives us a natural
language to discuss trajectories of orbits, a topic notorious for its
complexity. Certain interesting features arise from this structure. I will
describe how semi-local considerations lead to more global information and
symbolic dynamics. This is joint work with Umberto Hryniewicz and Gerhard
Knieper. The talk will address a general mathematical audience.

http://www.math.ias.edu/seminars/abstract?event=129431

3 Minimal Sets and Properties of Feral Pseudoholomorphic Curves 
   Joel Fish 

I will discuss some current joint work with Helmut Hofer, in which we define
and establish properties of a new class of pseudoholomorhic curves (feral
J-curves) to study certain divergence free flows in dimension three. In
particular, we show that if H is a smooth, proper, Hamiltonian on R^4, then
no non-empty regular energy level of H is minimal. That is, the flow of the
associated Hamiltonian vector field has a trajectory which is not dense.

http://www.math.ias.edu/seminars/abstract?event=137961

4 A Brief Tour of Proof Complexity: Lower Bounds and Open Problems 
   Toniann Pitassi 

I will give a tour of some of the key concepts and ideas in proof
complexity. First, I will define all standard propositional proof systems
using the sequent calculus which gives rise to a clean characterization of
proofs as computationally limited two-player games. I will also define
algebraic and semi-algebraic systems (SOS, IPS, Polynomial Calculus). 

Then we will see one or two (mostly) self-contained lower bounds, and
briefly mention how these lower bounds have been bootstrapped to prove lower
bounds for several classes of algorithms: Extended Formulations of linear
and semidefinite programs, monotone span programs, and monotone circuits.
Throughout, I will highlight some of my favorite longstanding
challenges/mysteries in the area.

http://www.math.ias.edu/seminars/abstract?event=129148

5 Gap and index estimates for Yang-Mills connections in 4-d 
   Matthew Gursky 

In this talk I want to discuss two related questions about the variational
structure of the Yang-Mills functional in dimension four. The first is the
question of 'gap' estimates; i.e., determining an energy threshold below
which any solution must be an instanton, hence a minimizer for the Y-M
energy. The second question is about non-minimal solutions, and in this case
the problem is to estimate the index of a solution. I will present some
recent work (joint with Kelleher and Streets) that attempts to address each
question when the base manifold has positive scalar curvature. I will also
mention some other geometric applications in 4-d.

http://www.math.ias.edu/seminars/abstract?event=141224

6 Properties of Feral Pseudoholomorphic Curves 
   Joel Fish 

I will discuss some technical details regarding properties of feral
pseuodoholomorphic curves, specifically those properties arising from
stretching constructions and as components of limit buildings arising from
attempts to compactify certain moduli spaces of finite energy curves. The
focus will be on those properties necessary to show the existence of a
closed invariant subset of any smooth compact hypersurface in R^4. These
properties will include exponential area bounds, the connected-local area
bound, and asymptotic curvature bounds.

http://www.math.ias.edu/seminars/abstract?event=143024

7 Multiplicity One Conjecture in Min-max theory 
   Xin Zhou 

I will present a proof with some substantial details of the Multiplicity One
Conjecture in Min-max theory, raised by Marques and Neves. It says that in a
closed manifold of dimension between 3 and 7 with a bumpy metric, the
min-max minimal hypersurfaces associated with the volume spectrum introduced
by Gromov, Guth, Marques-Neves are all two-sided and have multiplicity one. 

In particular, I will discuss three main parts of the proof, including: the
formulation of multiple-parameter min-max construction for hypersurfaces
with prescribed mean curvature (PMC), an approximation scheme (by PMC
min-max theory) of min-max construction of minimal hypersurfaces for
relative homotopy class of boundaries, and a topological argument to reduce
min-max construction for free homotopy class of mod-2 cycles to that for
relative homotopy class of boundaries.

http://www.math.ias.edu/seminars/abstract?event=141227

8 Equivariant and nonequivariant contact homology 
   Jo Nelson 

I will discuss joint work with Hutchings which constructs nonequivariant and
a family floer equivariant version of contact homology. Both theories are
generated by two copies of each Reeb orbit over Z and capture interesting
torsion information. I will then explain how one can recover the original
cylindrical theory proposed by Eliashberg-Givental-Hofer via our
construction.

http://www.math.ias.edu/seminars/abstract?event=143827

9 from dynamics to contact topology and back 
   Jo Nelson 

This is a light survey of the origins of contact topology and its
applications to dynamics. We will use anecdotes and images to illustrate
ideas.

http://www.math.ias.edu/seminars/abstract?event=141584

10 Front propagation in a nonlocal reaction-diffusion equation 
   Olga Turanova 

We consider a reaction-diffusion equation with a nonlocal reaction term.
This PDE arises as a model in evolutionary ecology. We study the regularity
properties and asymptotic behavior of its solutions.

http://www.math.ias.edu/seminars/abstract?event=142513

IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars

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